Scanning optical system

ABSTRACT

The invention relates to a scanning optical system of small size, which is constructed of a reduced number of optical elements. A scanning optical system  10  comprises a prism. In forward ray tracing from a light source  11  to an image plane (the surface to be scanned), a light beam from the light source is collimated by a condensing optical system constructed of a first transmitting surface  1 T, a second reflecting surface  1 R and a second transmitting surface  2 T into a substantially parallel light beam, which is then reflected and deflected at a two-dimensional scanner  12.  The reflected and deflected light forms an image through an image-formation optical system constructed of a third transmitting surface  3 T, a second reflecting surface  2 R, a third reflecting (total reflection) surface  3 R and a fourth transmitting surface  4 T for two-dimensional scanning of the surface to be scanned.

BACKGROUND OF THE INVENTION

[0001] The present invention relates generally to a scanning opticalsystem, and more particularly to a scanning optical system comprisingoptical deflection means for deflecting light coming from a lightsource, so that the surface to be scanned is two-dimensionally scanned.

[0002] Exemplary prior scanning optical systems are shown in FIGS. 10and 11. The scanning optical system shown in FIG. 10 (JP-A 08-327926)uses a condensing optical system comprising collimator lens 52, slit 53and cylindrical lens 54, through which light leaving light source 51 iscollimated and guided to rotary polygon mirror 55. The light reflectedand deflected at rotary polygon mirror 44 is directed to image-formationlens 56 composed of two lens elements, so that image-formation surface57 is subjected to one-dimensional scanning.

[0003] The scanning optical system shown in FIG. 11 (JP-A 08-146320)uses collimator lens 62 for collimating light leaving light source 61into a parallel light beam, which is then reflected and deflected bydeflection means 63, so that the surface 65 to be scanned is subjectedto two-dimensional scanning by image-formation means 64.

[0004] However, the optical system of FIG. 10, because of beingconstructed of a considerable number of optical elements, places strictlimitations on the precision of assembling and adjustment to achieve thenecessary optical performance, and incurs some added expenses as well.For the optical system of FIG. 11, on the other hand, nothing isdisclosed about its specific arrangement.

SUMMARY OF THE INVENTION

[0005] Having been accomplished to provide a solution to such problemswith the prior art as mentioned above, the present invention has for itsobject to provide a scanning optical system of small size, which isconstructed of a reduced number of optical elements.

[0006] According to the first aspect of the present invention, theaforesaid object is achieved by the provision of a scanning opticalsystem comprising optical deflection means for deflecting light from alight source to scan the surface to be scanned and an image-formationoptical system for focusing the light deflected by said opticaldeflection means on the surface to be scanned, thereby forming an imagethereon, characterized in that:

[0007] said image-formation optical system comprises an optical memberwherein a surface thereof having optical power and located nearest tothe surface to be scanned has a transmission function alone, and

[0008] said optical member comprises two or more reflecting surfaces,each of which has optical power and includes at least one rotationallyasymmetric surface decentered with respect to an axial chief ray.

[0009] This scanning optical system is exemplified by Examples 1 to 6given later.

[0010] The advantages (effects and actions) of the scanning opticalsystem according to the first aspect of the invention are now explained.By allowing the optical member to comprise two or more reflectingsurfaces, each of which has optical power and includes at least onerotationally asymmetric surface decentered with respect to an axialchief ray (hereinafter called the decentered, rotationally asymmetricsurface), the “turn-back” effect is obtained so that the size of theoptical system can be much more reduced than ever before. The reflectingsurfaces of optical power, because of having both a lens action and adeflection action, contribute significantly to size reductions.

[0011] Referring here to an optical system comprising a rotationallysymmetric reflecting surface having optical power and decentered withrespect to an axial chief ray, light rays strike obliquely on thatreflecting surface. Even with axial rays, accordingly, aberrations suchas comas and astigmatisms are produced due to decentration. Suchdecentration aberrations may be corrected by configuring this reflectingsurface in the form of a rotationally asymmetric surface as contemplatedherein.

[0012] A problem with a general scanning optical system is that whenlight deflected by optical deflection means is entered on a decentered,rotationally symmetric surface, it is impossible to ensure any linearscan capability. However, this linear scan capability can be ensured byconfiguring the reflecting surface of an image-formation optical systemin the form of a rotationally asymmetric reflecting surface.

[0013] Further, the use of the rotationally asymmetric surface enablesthe image-formation optical system to be formed of a two-dimensional farcsine θ lens or a two-dimensional fθ lens. Consequently, the surfaceto be scanned can be easily subjected to constant-speed, two-dimensionalscanning.

[0014] When optical deflection means with the angle of deflectionchanging linearly, such as a rotary polygon mirror, is used, an fθ lensmay be used as the image-formation optical system capable of producingminus distortions. Consequently, the surface to be scanned can bescanned at a constant speed. When optical deflection means with theangle of deflection changing sinusoidally, such as a galvanometermirror, is used, the image-formation optical system may be configured asan f arcsine θ lens by allowing it to produce distortions depending onthe magnitude of the angle of deflection (plus distortion when the angleof deflection is small, and minus distortion when the angle ofdeflection is large). Consequently, the surface to be scanned can besubjected to constant-speed scanning.

[0015] In this case, the surface of the image-formation optical system,which has optical power and is located nearest to the surface to bescanned, is effective for correction of distortions because there is alarge difference in light ray position between the angles of view, witha light beam of reduced diameter. It is noted that the function of thissurface on correction of distortions becomes worse if this surface isdesigned to have a function of transmitting light and a function ofreflecting light or to have a function of transmitting light and afunction of transmitting light, because some restrictive conditions areplaced on such a surface. It is noted that the surface formed of asingle surface and designed to produce a plurality of optical functionswill hereinafter called a combined surface. Thus, if that surface isdesigned to have a single optical function alone, i.e., only atransmission function as contemplated herein, it is then possible tomake effective correction for distortions. It is also easy to ensure theangle of view.

[0016] According to the second aspect of the present invention, thescanning optical system of the first aspect is further characterized inthat said optical member is configured in the form of a prism member.

[0017] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0018] The advantages of the scanning optical system are now explained.Generally speaking, a reflecting surface must be more strictlycontrolled in terms of decentration errors than a refracting surface,and so its adjustment on assembling is an onerous task. However, if thereflecting surface of the optical member is configured as one surface ofthe prism member, then this problem can be solved because the wholepositioning of the reflecting surface becomes easy.

[0019] Light rays incident from the deflection means on the prism memberare refracted at the entrance surface of the prism member, so that theheights of off-axis light rays incident on the subsequent surfaces canbe kept low. It is thus possible to reduce the size of the opticalsystem and achieve a larger angle of view as well. In addition, theheight of light rays depending on the off-axis light rays becomes so lowthat comas or the like can be reduced.

[0020] According to the third aspect of the invention, the scanningoptical system of the first aspect is further characterized in that saidoptical member comprises at least one surface which has a function oftransmitting light and a function of reflecting light. This surfaceshould preferably be defined by a surface other than that locatednearest to the surface to be scanned.

[0021] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0022] The advantages of the scanning optical system are now explained.Since the two functions, transmission and reflection, occur at the samesurface, the number of surfaces that form the image-formation system canbe so reduced that it can be simplified and reduced in size. Morepreferably in this case, the reflection function should be totalreflection function. When reflection at the combined surface isreflection at a reflecting film rather than total reflection, it isnecessary to form the reflecting film for the reflecting surface atanother position separate from a transmitting area for a transmittingsurface, offering problems such as an increase in the size of theoptical system and increased aberrations. In addition, the need offabricating the reflecting film leads to added cost.

[0023] According to the fourth aspect of the invention, the scanningoptical system of the second aspect is further characterized in thatsaid prism member comprises three surfaces inclusive of one combinedtransmitting and reflecting surface.

[0024] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0025] The advantages of the scanning optical system are now explained.When a prism member is used for the second scanning optical system ofthe invention, it should comprise at least an entrance surface, tworeflecting surfaces and an exit surface. However, if at least threesurfaces, i.e., a combined surface, a transmitting surface and areflecting surface, are used to construct the prism member, then theprism member can be simplified in construction and reduced in size.

[0026] According to the fifth aspect of the invention, there is provideda scanning optical system comprising a condensing optical system forcollimating a light beam from a light source into a substantiallyparallel beam, optical deflection means for deflecting light emergingfrom said condensing optical system for scanning the surface to bescanned, and an image-formation optical system for focusing lightdeflected by said optical deflection means on the surface to be scanned,thereby forming an image thereon, characterized in that:

[0027] a final surface of said condensing optical system, through whicha light beam leaving said condensing optical system is entered into saidoptical deflection means, and a first surface of said image-formationoptical system, through which a light beam is entered from said opticaldeflection means into said image-formation optical system, are definedby the same surface.

[0028] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0029] The advantages of the scanning optical system are now explained.In forward ray tracing from the light source to the surface to bescanned, when the “final surface that forms the condensing opticalsystem” and the “first surface of the image-formation optical system”,which are the surfaces located before and after the optical deflectionmeans, are configured as separate surfaces, two such surfaces must belocated at separate positions; that is, it is required to space thesurface located before the optical deflection means away from thesurface located after the same or increase the angle of incidence oflight rays on the optical deflection means.

[0030] However, as the surfaces located before and after the opticaldeflection means are spaced away from each other, the size of theoptical system becomes large. As the angle of incidence of light rays onthe optical deflection means increases, on the other hand, the area ofthe optical deflection means becomes large and so makes it difficult toensure large angles of deflection or high deflection frequencies(scanning frequencies). In particular, this offers a grave problem withoptical deflection means constructed of a single reflecting surface, asis the case with a micromachined scanner fabricated making use of suchmicromachining as set forth in JP-A 10-20226.

[0031] If the surfaces located before and after the optical deflectionmeans are defined by the same surface, it is then possible to make theangle of incidence of light rays on the optical deflection means sosmall that the area of the optical deflection means can be decreased,thereby increasing the angle of deflection of the optical deflectionmeans or achieving high deflection frequencies (scanning frequencies).

[0032] According to the sixth aspect of the invention, the scanningoptical system of the fifth aspect is further characterized in thatoptically functional surfaces located before and after said opticaldeflection means are defined by transmitting surfaces.

[0033] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0034] The advantages of the scanning optical system are now explained.In the forward ray tracing from the light source to the surface to bescanned, when the optically active surfaces located before and after theoptical deflection means are defined by reflecting surfaces, both thefinal surface (reflecting surface 1) that forms the condensing opticalsystem and the first surface (reflecting surface 2) that forms theimage-formation optical system take the form of reflecting surfaces. Inorder to allow incident light on the reflecting surface 1 to arrive atthat reflecting surface while unobstructed by the reflection typeoptical deflection means, it is necessary to increase the angle ofincidence of light rays on the reflection type optical deflection means,increase the distance between the surfaces (reflecting surface1=reflecting surface 2) located before and after the reflection typeoptical deflection means and the optical deflection means or make anangle between the entrance surface with respect to the opticaldeflection means and the primary scanning surface (both surfaces are notparallel with each other). This holds true for the case where lightreflected at the reflecting surface 2 emerges while unobstructed by thereflection type optical deflection means. Whatever the case may be,however, there are several problems such as an increase in the area ofthe optical deflection means, an increase in the size of the opticalsystem, and difficulty in making correction for decentrationaberrations.

[0035] If the optically active surfaces located before and after theoptical deflection means are configured as transmitting surfaces, thensuch problems can be overcome.

[0036] According to the seventh aspect of the invention, the scanningoptical system of the fifth aspect is further characterized in that saidimage-formation optical system comprises at least one combinedtransmitting and reflecting surface.

[0037] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0038] The advantages of the scanning optical system are now explained.Since the two actions, transmission and reflection, occur at the samesurface, the number of surfaces that form the image-formation system canbe so reduced that it can be simplified in construction and reduced insize. More preferably in this case, the reflection action should betotal reflection action. When reflection at the combined surface isreflection at a reflecting film rather than total reflection, it isnecessary to form the reflecting film for the reflecting surface atanother position separate from a transmitting area for a transmittingsurface, offering problems such as an increase in the size of theoptical system and increased aberrations. In addition, the need offabricating the reflecting film leads to added cost.

[0039] According to the eighth aspect of the invention, there isprovided a scanning optical system comprising a condensing opticalsystem for collimating a light beam from a light source into asubstantially parallel beam, optical deflection means for deflectinglight emerging from said condensing optical system for scanning thesurface to be scanned, and an image-formation optical system forfocusing light deflected by said optical deflection means into thesurface to be scanned, thereby forming an image thereon, characterizedin that:

[0040] said scanning optical system comprises a prism member, and saidprism member includes at least a portion of said condensing opticalsystem, and at least a portion of said image-formation optical system.

[0041] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0042] The advantages of the scanning optical system are now explained.Since a portion of the condensing optical system and a portion of theimage-formation optical system are configured with a single opticalelement, the number of parts that form the scanning optical system canbe reduced. Consequently, the operation for position control onassembling for achieving the desired performance becomes easy, resultingin cost reductions.

[0043] According to the ninth aspect of the invention, the scanningoptical system of the eighth aspect is further characterized in thatsaid image-formation optical system comprises one prism member.

[0044] This scanning optical system is exemplified by Examples 1-3 andExample 6 given later.

[0045] With the ninth scanning optical system, the advantages of theeighth scanning optical system are much more enhanced.

[0046] According to the tenth aspect of the invention, a scanningoptical system comprising a condensing optical system for collimating alight beam from a light source into a substantially parallel beam,optical deflection means for deflecting light emerging from saidcondensing optical system for scanning the surface to be scanned, and animage-formation optical system for focusing light deflected by saidoptical deflection means into the surface to be scanned, thereby formingan image thereon, as recited in any one of the 1st, 5th and 8th aspectsof the invention is further characterized in that a total of at leastthree reflections occur at said condensing optical system and saidimage-formation optical system.

[0047] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0048] The advantages of the scanning optical system are now explained.A total of at least three reflections enhance the “turn-back” effect, sothat the effect on reducing the overall size of the scanning opticalsystem is much more augmented.

[0049] According to the 11th aspect of the invention, the scanningoptical system of the 8th aspect is further characterized in that saidprism member including at least a portion of said condensing opticalsystem, and at least a portion of said image-formation optical systemhas a combined transmitting and reflecting surface.

[0050] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0051] The advantages of the scanning optical system are now explained.Since the two actions, transmission and reflection, occur at the samesurface, the number of surfaces that form the optical system can be soreduced that it can be simplified construction and reduced in size. Morepreferably in this case, the reflection action should be totalreflection action. When reflection at the combined surface is reflectionat a reflecting film rather than total reflection, it is necessary toform the reflecting film for the reflecting surface at another positionseparate from a transmitting area for a transmitting surface, offeringproblems such as an increase in the size of the optical system andincreased aberrations. In addition, the need of fabricating thereflecting film leads to added cost.

[0052] According to the 12th aspect of the invention, the scanningoptical system of the 11th aspect is further characterized in that saidprism member including at least a portion of said beam-condensingoptical system, and at least a portion of said image-formation opticalsystem has a combined transmitting and reflecting surface capable ofthree optical actions, i.e., two transmissions and one reflection.

[0053] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0054] Referring to the advantages of the scanning optical system, thenumber of surfaces that form the scanning optical system can be muchsmaller than that of the 11th scanning optical system. If the surface ofthe prism member facing the optical deflection means is defined by sucha combined surface, it is then possible to obtain the advantages of the5th scanning optical system.

[0055] According to the 13th aspect of the invention, the 8th scanningoptical system wherein said prism member comprises at least a portion ofsaid condensing optical system, and at least a portion of saidimage-formation optical system is further characterized in that:

[0056] the portion of said condensing optical system included in saidprism member comprises at least three surfaces, an entrance surface forsaid prism member, a rotationally asymmetric reflecting surface that hasoptical power and is decentered with respect to an axial chief ray, andan exit surface from said prism member, and

[0057] the portion of said image-formation optical system included insaid prism member comprises at least three surfaces, a reentrancesurface for said prism member, a rotationally asymmetric reflectingsurface that has optical power and is decentered with respect to anaxial chief ray, and an re-exit surface from said prism member.

[0058] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0059] The reflecting surfaces, each having optical power, have both alens action and a deflection action, and so are greatly effective forreducing the size of the optical system. Since both the condensingoptical system and the image-formation optical system can be reduced insize, the overall size of the present scanning optical system can bereduced.

[0060] Referring here to an optical system comprising a reflectingsurface having optical power and decentered with respect to an axialchief ray, light rays strike obliquely on that decentered reflectingsurface. Even with axial rays, accordingly, aberrations such as comasand astigmatisms are produced due to decentration. Such decentrationaberrations may be corrected by configuring this reflecting surface inthe form of a rotationally asymmetric surface.

[0061] A problem with a general scanning optical system is that whenlight deflected by optical deflection means is entered on a decenteredsurface, it is impossible to ensure linear scan capability. However,this linear scan capability can be ensured by configuring the reflectingsurface of an image-formation optical system in the form of arotationally asymmetric reflecting surface. Further, the use of therotationally asymmetric surface enables the image-formation opticalsystem to be formed of a two-dimensional f arcsine θ lens or atwo-dimensional fθ lens. Consequently, the surface to be scanned can beeasily subjected to constant-speed scanning.

[0062] With the rotationally asymmetric reflecting surface used at theportion of the condensing optical system included in the prism member,it is possible to achieve the function of shaping beams from a lightsource of oval shape in section such as an LD and the function ofcorrecting field tilts.

[0063] Generally speaking, a reflecting surface must be more strictlycontrolled in terms of decentration errors than a refracting surface,and so its adjustment on assembling is an onerous task. However, if thereflecting surface of the optical member is configured as one surface ofthe prism member, then any adjustment operation for that reflectingsurface can be dispensed with.

[0064] Light rays incident from the deflection means on the portion ofthe image-formation optical system of the prism member are refracted atthe entrance surface of the prism member, so that the heights ofoff-axis light rays incident on the subsequent surfaces can be kept low.It is thus possible to reduce the size of the optical system and achievea larger angle of view as well. In addition, the heights of light raysfollowing the off-axis light rays become so low that comas or the likecan be reduced.

[0065] According to the 14th aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that the rotationally asymmetric surface of saidimage-formation optical system has only one symmetric plane with respectto shape.

[0066] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0067] The advantages of the scanning optical system are that thesymmetric plane with respect to shape makes great contributions toproductivity.

[0068] According to the 15th aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that the rotationally asymmetric surface of saidbeam-condensing optical system has only one symmetric plane with respectto shape.

[0069] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0070] Referring to the advantages of the scanning optical system, thesame advantages as in the 13th scanning optical system are obtained bythe action and effect of the rotationally asymmetric surface, and thesame advantages as in the 14th scanning optical system are obtained bythe action and effect due to the incorporation of one symmetric planewith respect to shape. Thus, this embodiment is preferred in that thecondensing optical system has such advantages as mentioned above.

[0071] According to the 16th aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that the rotationally asymmetric surface of saidimage-formation optical system is defined by a free-form surface havingonly one symmetric plane with respect to shape.

[0072] This scanning optical system is exemplified by Examples 1-6 givenlater.

[0073] The advantages of the scanning optical system are now explained.The free-form surface used herein is defined by the following formula(a), and the axis of the free-form surface is given by the Z axis forthat defining formula. $\begin{matrix}{Z = {{{cr}^{2}/\left\lbrack {1 + {\sqrt{\quad}\left\{ {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\}}} \right\rbrack} + {\sum\limits_{j = 2}^{66}{C_{j}X^{m}Y^{n}}}}} & (a)\end{matrix}$

[0074] Here the first term of formula (a) is a spherical surface term,and the second term is a free-form surface term.

[0075] In the spherical surface term, c is the curvature of an apex, Kis a conic constant, and r={square root}(X²+Y²).

[0076] The free-form surface term is $\begin{matrix}{\sum\limits_{j = 2}^{66}{C_{y}X^{m}Y^{n}}} \\\begin{matrix}{Z = {{C_{2}X} + {C_{3}Y} + {C_{4}X^{2}} + {C_{5}{XY}} + {C_{6}Y^{2}} + {C_{7}X^{3}} + {C_{8}X^{2}Y} + {C_{9}{XY}^{2}} +}} \\{{{C_{10}Y^{3}} + {C_{11}X^{4}} + {C_{12}X^{3}Y} + {C_{13}X^{2}Y^{2}} + {C_{14}{XY}^{3}} + {C_{15}Y^{4}} + {C_{16}X^{5}} +}} \\{{{C_{17}X^{4}Y} + {C_{18}X^{3}Y^{2}} + {C_{19}X^{2}Y^{3}} + {C_{20}{XY}^{4}} + {C_{21}Y^{5}} + {C_{22}X^{6}} +}} \\{{{C_{23}X^{5}Y} + {C_{24}X^{4}Y^{2}} + {C_{25}X^{3}Y^{3}} + {C_{26}X^{2}Y^{4}} + {C_{27}{XY}^{5}} + {C_{28}Y^{6}} +}} \\{{{C_{29}X^{7}} + {C_{30}X^{6}Y} + {C_{31}X^{5}Y^{2}} + {C_{32}X^{4}Y^{3}} + {C_{33}X^{3}Y^{4}} + {C_{34}X^{2}Y^{5}} +}} \\{{{C_{35}{XY}^{6}} + {C_{36}Y^{7}}}}\end{matrix}\end{matrix}$

[0077] Here C_(j) (j is an integer of 2 or greater) is a coefficient.

[0078] In general, the aforesaid free-form surface has no symmetricplane at both the X-Z plane and the Y-Z plane. However, by reducing allthe odd-numbered terms for X to zero, that free-form surface can haveonly one symmetric plane parallel with the Y-Z plane. For instance, thismay be achieved by reducing to zero the coefficients for the terms C₂,C₅, C₇, C₉, C₁₂, C₁₄, C₁₆, C₁₈, C₂₀, C₂₃, C₂₅, C₂₇, C₂₉, C₃₁, C₃₃, C₃₅,. . . .

[0079] By reducing all the odd-numbered terms for Y to zero, thefree-form surface can have only one symmetric plane parallel with theX-Z plane. For instance, this may be achieved by reducing to zero thecoefficients for the terms C₃, C₅, C₈, C₁₀, C₁₂, C₁₄, C₁₇, C₁₉, C₂₁,C₂₃, C₂₅, C₂₇, C₃₀, C₃₂, C₃₄, C₃₆, . . . .

[0080] By using any one of the aforesaid symmetric planes and deflectingit in that symmetric plane direction, rotationally asymmetricaberrations produced due to decentration are effectively correctedwhile, at the same time, productivity is improved.

[0081] It is here noted that the free-form surface may be defined byother defining formulae such as Zernike polynomial.

[0082] According to the 17th aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that said optical deflection means is defined by asingle two-dimensional optical deflecting means capable oftwo-dimensional deflection by itself.

[0083] This scanning optical system is exemplified by Examples 1-5 givenlater.

[0084] The advantages of the scanning optical system are now explained.To make the area of the optical deflection means small, the opticaldeflection means must be located in the vicinity of the entrance pupilof the image-formation optical system. Consider the case where twoone-dimensional optical deflection means are used for two-dimensionalscanning. To diminish the size of the optical deflection means, the twoone-dimensional deflection means must be located in conjugativerelations to each other or the spacing between them must be narrowed,resulting in problems that the construction of the optical systembecomes complicated and large, restrictive conditions for the layout ofthe optical system increase, etc. With a single optical deflection meanscapable of two-dimensional deflection, the optical system can be soeasily laid out that it can be reduced in size and simplified inconstruction.

[0085] According to the 18th aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that said optical deflection means has a sinusoidallychanging angle of deflection.

[0086] This scanning optical system corresponds to Examples 1, 2, 4, 5and 6 given later as well as to Example 3 provided that electricalcorrection of image distortions must be made.

[0087] The advantages of the scanning optical system are now explained.For instance, a micromachined scanner fabricated making use of suchmicromachining as set forth in JP-A 10-20226 comprises a singlereflecting mirror. Upon high-speed scanning, this reflecting mirrorvibrates sinusoidally to reflect and deflect light. With such opticaldeflection means, not only are size and cost reductions achievable butalso high-speed scanning is achievable with reduced power consumption.If, in this case, the image-formation optical system of the scanningoptical system is configured in the form of an f arcsine θ lens, it isthen possible to carry out constant-speed scanning for the surface to bescanned.

[0088] According to the 19th aspect of the invention, the scanningoptical system of the 18th aspect is further characterized in that saidoptical deflection means having a sinusoidally changing angle ofdeflection is capable of using up to 95% of the amplitude of an angle ofdeflection of light for scanning.

[0089] This scanning optical system corresponds to Examples 1, 2, 4, 5and 6 given later as well as to Example 3 provided that electricalcorrection of image distortions must be made.

[0090] The advantages of the scanning optical system are now explainedwith reference to a reflection type deflector such as a galvanometermirror. As shown in FIG. 9(a), consider the case where there is used areflection type deflector (reflection type deflection means) wherein thedeflection angle θ of its reflecting surface from a reference reflectingsurface changes sinusoidally. To carry out constant-speed scanningwithout recourse to any electrical correction of image distortions, itis then required that the image-formation optical system be configuredin the form of an f arcsine θ lens.

[0091] Here assume that with deflecting means wherein the deflectionangle of its reflecting surface changes sinusoidally at an amplitudeφ₀/k, the surface to be scanned is scanned making use of a deflectionangle (±φ₀) that is k times as large as the amplitude of the deflectionangle of the reflecting surface. To configure the image-formationoptical system in the form of an f arcsine θ lens, it is then requiredto satisfy the following condition (0<k≦−1):

Image Height y=f·2(φ₀ /k)arcsin{φ/(φ₀ /k)}

[0092] To configure the image-formation system in the form of an farcsine θ lens well fit for the whole range of an angle of deflection ofabout ±20°, it is necessary to produce some considerable plusdistortions, rendering the design of the image-formation systemdifficult. By making use of only an area where the linearity of φ/(φ₀/k)is better, however, it is easy to configure the image-formation systemas an f arcsine θ lens.

[0093] At k≦0.95, the linearity of φ/(φ₀/k) is at most about half thatin the case of k=1, so that it is easy to configure the image-formationoptical system as an f arcsine θ lens. It is thus possible to simplifythe optical system with size reductions.

[0094] As is the case of a conventional display having a blankinginterval of the order of 17%, a scanning optical system, too, cannotutilize the whole range of the angle of deflection by reason ofelectrical processing. In the present invention, however, the upperlimit to the amplitude of the angle of deflection of the deflectionmeans is about 95% because images can be displayed without recourse toan ordinary display.

[0095] As shown in FIG. 9(b), the foregoing explanation goes true for atransmission type of optical deflection means such as an acousto-opticdeflector ADO; however, it is noted that the angle of deflection isgiven by 2φ.

[0096] According to the 20th aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that constant-speed scan capability is electricallycorrected.

[0097] This scanning optical system may be embodied as desired.

[0098] The advantages of the 20th scanning optical system are nowexplained. Especially when, on two-dimensional scanning, two-dimensionallinear scan capability and constant-speed scan capability are ensured byallowing the image-formation optical system to produce suitabledistortion in conformity with the deflection characteristics of theoptical deflection means, the scanning optical system becomescomplicated and large. On two-dimensional scanning at high speed, on theother hand, it is difficult to make electrical, real-time correction forimage distortions due to linear scan capability, because that correctionis two-dimensional one.

[0099] If the linear scan capability is ensured by the image-formationoptical system and constant-speed scan capability is done by electricalcorrection, then the scanning optical system can be simplified inconstruction and reduced in size. In addition, the scanning opticalsystem is compatible with high-speed scanning because the imagedistortions can be electrically corrected per scanning line in the mainscanning direction.

[0100] In this case, when all of the amplitude of the sinusoidallychanging angle of deflection is harnessed, there is too large a scanningspeed difference between in the vicinity of the center of an image to bescanned at high speed and in the vicinity of the periphery of an imageto be scanned at low speed. Consequently, even when electricalcorrection of image distortions is made, it is difficult to make thatcorrection with high precision. It is thus preferable to make use ofabout 85% of the amplitude of the angle of deflection, becausecorrection of the constant-speed scan capability is improved inapproximately two steps.

[0101] According to the 21st aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that the angle of deflection by said optical deflectingmeans changes linearly.

[0102] This scanning optical system is exemplified by Example 3 givenlater (and corresponds to Examples 1, 2 and 4-6, too, with the provisothat image distortions are electrically corrected).

[0103] The advantages of the scanning optical system are now explained.The rotary polygon mirror rotates at a constant speed, and so the angleof optical deflection changes linearly. If the rotary polygon mirror isused as optical deflection means, it is then possible to ensure a largeangle of deflection with that optical deflection means and make thefield angle of the scanning optical system large. At this time, if an fθlens is used as the image-formation optical system for the scanningoptical system, the surface to be scanned can then be scanned at aconstant speed.

[0104] According to the 22nd aspect of the invention, the scanningoptical system of any one of the 1st, 5th and 8th aspects is furthercharacterized in that said-image formation optical system has only onesymmetric plane with respect to shape and is decentered only in saidsymmetric plane with respect to plane, said scanning optical systemsatisfying the following formula:

φ₂θ₁/φ₁θ₂<1  (1)

[0105] Here θ₂ is the half field angle of the image-formation opticalsystem in a symmetric plane direction on the side of the surface to bescanned, θ₁ is the half field angle of the image-formation opticalsystem in a plane direction perpendicular to the symmetric plane, 2φ₂ isthe one-side angle of deflection of the optical deflecting means neededfor scanning of the surface to be scanned in the symmetric planedirection, and 2φ₁ is the one-side angle of deflection of the opticaldeflecting means necessary for scanning of the surface to be scanned ina plane direction perpendicular to the symmetric plane.

[0106] This formula indicates that when it comes down to such reflectiontype deflecting means as a polygon or galvanometer mirror, the one-sidedeflection angle of the reflecting mirror necessary for scanning isgiven by φ₁, and φ₂. The one-side deflection angle of the reflectingmirror, used herein, is understood to refer to a maximum angle ofdeviation from the surface of the reflecting mirror corresponding to thecenter of the surface to be scanned; however, this does not always meanthat the optical deflection means, i.e., the reflecting mirror deflects±φ. To put it another way, when a part of the amplitude of thereflecting mirror is used to scan the surface to be scanned, thedeflection angle used therefor is ±φ. For such a transmission type ofoptical deflecting means as an acousto-optical deflector AOD, theone-side angle of deflection is represented by 2φ₁ and 2φ₂ (see FIG. 9).This scanning optical system is exemplified by Examples 1-6 given later.

[0107] The advantages of this scanning optical system are now explainedwith reference to such a reflection type of optical deflection means asa polygon or galvanometer mirror (see FIG. 9(a)). Here assume that whenthe one-side deflection angle of the reflection type optical deflectionmeans is φ (or when the angle of deflection is 2φ), the half field angleon scanning of the image-formation optical system is θ. Then, the pupilmagnification of the image-formation optical system upon forward raytracing is given by 2φ/θ.

[0108] As already set forth herein, it is preferable that theimage-formation optical system has only one symmetric plane with respectto shape, and is decentered in that symmetric plane alone, because theproductivity of the image-formation optical system is improved with costreductions. In this case, it is easy to ensure a wide field angle in thedirection vertical to the symmetric plane with respect to shape, and soit is desired that this direction be determined as the scanningdirection of a one-dimensional scanning optical system or as a directionin which the scanning field angle of a two-dimensional optical systembecomes large. It is then noted that the image-formation optical systemis difficult to construct, because the optical system must be designedin such a way that the decentered surface of the image-formation opticalsystem does not interfere with the rest in the plane direction in whichthe image-formation optical system is decentered.

[0109] To remove such difficulty, it is preferable that the pupilmagnification of the image-formation optical system in the direction inwhich it is decentered (in the symmetric plane direction of theimage-formation optical system with respect to shape) is smaller thanthat in the direction vertical to the symmetric plane, thereby reducingthe beam spread angle in the image-formation optical system, because itis easier to construct the image-formation optical system.

[0110] More specifically, it is desired to satisfy the followingformula:1 > pupil  magnification  in  the  symmetric  plane/pupil  magnification  in  the  plane  vertical  to  the  symmetric  plane = (2  φ₂/θ₂)/(2  φ₁/θ₁) = φ₂θ₁/φ₁θ₂

[0111] When the symmetric plane direction of the image-formation opticalsystem with respect to shape is determined as the sub-scanning directionand the direction vertical to the symmetric plane as the main scanningdirection, the resolving power of the image-formation optical system inthe main scanning direction must be made equal to that in thesub-scanning direction by making the size of the optical deflectionmeans in the sub-scanning direction larger than that in the mainscanning direction. This image-formation optical system is wellcompatible with high-speed scanning because of a decrease in its size inthe main scanning direction in which high-speed scanning is necessaryfor two-dimensional scanning.

[0112] According to the 23rd aspect of the invention, the scanningoptical system of the 22nd aspect is further characterized by satisfyingthe following condition:

NA2/NA1>1  (2)

[0113] Here NA2 is the numerical aperture of a light beam that isincident from the light source in the symmetric plane direction withrespect to shape on the condensing optical system, and NA1 is thenumerical aperture of a light beam that is incident from the lightsource in the direction vertical to the symmetric plane with respect toshape on the condensing optical system.

[0114] This scanning optical system is embodied by Examples 1-6 givenlater.

[0115] The advantages of the scanning optical system are now explained.When the symmetric plane direction of the image-formation optical systemwith respect to shape is determined as the sub-scanning direction andthe direction vertical to the symmetric plane as the main scanningdirection, the resolving power of the image-formation optical system inthe main scanning direction must be made equal to that in thesub-scanning direction by making the size of the optical deflectionmeans in the sub-scanning direction larger than that in the mainscanning direction.

[0116] In order that the light leaving the light source has theaforesaid shape at the scanning means, it is preferable to satisfycondition (2) because the condensing optical system is easier toconstruct.

[0117] Still other objects and advantages of the invention will in partbe obvious and will in part be apparent from the specification.

[0118] The invention accordingly comprises the features of construction,combinations of elements, and arrangement of parts which will beexemplified in the construction hereinafter set forth, and the scope ofthe invention will be indicated in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0119]FIG. 1 is an optical path diagram for Example 1 of the scanningoptical system according to the present invention.

[0120]FIG. 2 is illustrative of one example of the construction of aplurality of monochromatic light sources used for color displays.

[0121]FIG. 3 is a plan schematic of one example of a two-dimensionalmicromachined scanner.

[0122]FIG. 4 is an optical path diagram for Example 2 of the scanningoptical system according to the present invention.

[0123]FIG. 5 is an optical path diagram for Example 3 of the scanningoptical system according to the present invention.

[0124]FIG. 6 is an optical path diagram for Example 4 of the scanningoptical system according to the present invention.

[0125]FIG. 7 is an optical path diagram for Example 5 of the scanningoptical system according to the present invention.

[0126]FIG. 8 is an optical path diagram for Example 6 of the scanningoptical system according to the present invention.

[0127]FIG. 9(a) is illustrative of the basic construction of areflection type of optical deflection means, and FIG. 9(b) isillustrative of the basic construction of a transmission type of opticaldeflection means.

[0128]FIG. 10 is illustrative of the construction of anotherconventional scanning optical system.

[0129]FIG. 11 is illustrative of the construction of yet anotherconventional scanning optical system.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0130] Examples 1 through 6 of the scanning optical system according tothe present invention are now explained with reference to theaccompanying drawings.

[0131] In what follows, the main scanning direction is defined by anX-direction and the sub-scanning direction by a Y-direction.

[0132] Constitutional parameters obtained in back ray tracing for eachexample will be enumerated later. In the constitutional parameters, anaxial chief ray 1 is defined by a light ray passing vertically throughthe center of the surface to be scanned (not shown) and arriving at thecenter of a light source 11 via optical deflection means 12 upon backray tracing, as shown in FIG. 1.

[0133] In the back ray tracing, the first surface 4T returned back to anon-decentered state (although actually decentered in the Y-direction)is defined as the origin of the decentered optical system. The Z-axisdirection is defined by a direction along the axial chief ray 1; thepositive Z-axis direction by a direction from the surface to be scannedtoward the first surface 4T of the optical system 10; the Y-Z plane (aplane in FIG. 1) by a plane including this Z-axis and the center of thesurface to be scanned; the positive X-axis direction by a direction thatpasses through the origin, intersects perpendicularly with the Y-Z planeand turns from before the paper toward the back direction; and theY-axis by an axis that forms a right-handed orthogonal coordinatesystem. This coordinate system is shown in FIG. 1. However, such acoordinate system is not given for FIGS. 4 to 8 that show otherexamples.

[0134] Given for a decentered surface are the amount of decentration ofthe apex of that surface from the center of the origin of the aforesaidcoordinate system (in the X, Y and Z-axis directions represented by X, Yand Z) and the angles (α, β, γ(°)) of tilt of the center axis (the Zaxis in the following formula (a) for a free-form surface) with respectto the X-axis, the Y-axis, and the Z-axis, respectively. It is herenoted that the positive α and β mean counterclockwise rotation withrespect to the positive directions of the respective axes, and thepositive γ means clockwise rotation with respect to the positivedirection of the Z axis.

[0135] In Examples 1 to 6, each surface is decentered in this Y-Z plane,and only one symmetric plane for each rotationally asymmetric free-formsurface is given by the Y-Z plane.

[0136] Regarding the optically active surfaces forming the opticalsystem of each example, when a specific surface (including a virtualsurface) and the subsequent surface form a coaxial optical system, asurface spacing is given. Besides, the refractive indices of media andAbbe's numbers are given as usual.

[0137] The free-form surface used herein is of such a shape as definedby the aforesaid equation (a), and the Z-axis of that defining equationis the axis of the free-form surface.

[0138] The DOE (diffractive optical element) is designed by Sweattmethod (an ultra-high index method) (W. C. Sweatt, “Mathematicalequivalence between a holographic optical element and an ultra-highindex lens”, J. Opt. Soc. Am., Vol. 69, No. 3(1979) at a referencewavelength=587.56 nm (d-line), at which the refractive index of anultra-high index lens=1001 and the Abbe constant=−3.45.

[0139] It is here noted that the term with respect to freeform surfaceswith no data is zero. The refractive index is given with respect tod-line (587.56 nm wavelength), and the length and angle are given in mmand °.

[0140] Among other formulae for defining the free-form surface, there isZernike polynomial, given below. The shape of this surface is given bythe following formula. The axis for Zernike polynomial is given by the Zaxis for the defining formula. The rotationally asymmetric surface isdefined by polar coordinates for the height of the Z axis with respectto the X-Y plane provided that R is the distance from the Z axis withinthe X-Y plane and A is the azimuth angle round the Z axis, as expressedby the angle of rotation measured from the X-axis.

x=R×cos(A)

y=R×sin(A) $\begin{matrix}\begin{matrix}{Z = {D_{2} + {D_{3}R\quad {\cos (A)}} + {D_{4}R\quad {\sin (A)}} + {D_{5}R^{2}{\cos \left( {2A} \right)}} +}} \\{{{D_{6}\left( {R^{2} - 1} \right)} + {D_{7}R^{2}{\sin \left( {2A} \right)}} + {D_{8}R^{3}{\cos \left( {3A} \right)}} +}} \\{{{{D_{9}\left( {{3R^{3}} - {2R}} \right)}{\cos (A)}} + {{D_{10}\left( {{3R^{3}} - {2R}} \right)}{\sin (A)}} +}} \\{{{D_{11}R^{3}{\sin \left( {3A} \right)}} + {D_{12}R^{4}{\cos \left( {4A} \right)}} + {{D_{13}\left( {{4R^{4}} - {3R^{2}}} \right)}{\cos \left( {2A} \right)}} +}} \\{{{D_{14}\left( {{6R^{4}} - {6R^{2}} + 1} \right)} + {{D_{15}\left( {{4R^{4}} - {3R^{2}}} \right)}{\sin \left( {2A} \right)}} +}} \\{{{D_{16}R^{4}{\sin \left( {4A} \right)}} + {D_{17}R^{5}{\cos \left( {5A} \right)}} + {{D_{18}\left( {{5R^{5}} - {4R^{3}}} \right)}{\cos \left( {3A} \right)}} +}} \\{{{{D_{19}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}{\cos (A)}} +}} \\{{{{D_{20}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}{\sin (A)}} + {{D_{21}\left( {{5R^{5}} - {4R^{3}}} \right)}{\sin \left( {3A} \right)}} +}} \\{{{D_{22}R^{5}{\sin \left( {5A} \right)}} + {D_{23}R^{6}{\cos \left( {6A} \right)}} + {{D_{24}\left( {{6R^{6}} - {5R^{4}}} \right)}{\cos \left( {4A} \right)}} +}} \\{{{{D_{25}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}{\cos \left( {2A} \right)}} +}} \\{{{D_{26}\left( {{20R^{6}} - {30R^{4}} + {12R^{2}} - 1} \right)} +}} \\{{{{D_{27}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}{\sin \left( {2A} \right)}} +}} \\{{{{D_{28}\left( {{6R^{6}} - {5R^{4}}} \right)}{\sin \left( {4A} \right)}} + {D_{29}R^{6}{\sin \left( {6A} \right)}}}}\end{matrix} & (b)\end{matrix}$

[0141] It is noted that when this free-form surface is designed in theform of an optical system symmetric in the X-axis direction, D₄, D₅, D₆,D₁₀, D₁₁, D₁₂, D₁₃, D₁₄, D₂₀, D₂₁, D₂₂, . . . are used.

[0142] Besides, there is the following defining formula:

Z=ΣΣC _(nm) XY

[0143] When expanded with respect to k=7 (the seventh term) as anexample, this may be expressed by the following formula: $\begin{matrix}\begin{matrix}{Z = {C_{2} + {C_{3}Y} + {C^{4}{X}} + {C_{5}Y^{2}} + {C_{6}Y{X}} + {C_{7}X^{2}} + \quad {C_{8}Y^{3}} +}} \\{{{C_{9}Y^{2}{X}} + {C_{10}{YX}^{2}} + {C_{11}{X^{3}}} + {C_{12}Y^{4}} + {C_{13}Y^{3}{X}} +}} \\{{{C_{14}Y^{2}X^{2}} + {C_{15}Y{X^{3}}} + {C_{16}X^{4}} + {C_{17}Y^{5}} + {C_{18}Y^{4}{X}} +}} \\{{{C_{19}Y^{3}X^{2}} + {C_{20}Y^{2}{X^{3}}} + {C_{21}{YX}^{4}} + {C_{22}{X^{5}}} + {C_{23}Y^{6}} +}} \\{{{C_{24}Y^{5}{X}} + {C_{25}Y^{4}X^{2}} + {C_{26}Y^{3}{X^{3}}} + {C_{27}Y^{2}X^{4}} +}} \\{{{C_{28}Y{X^{5}}} + {C_{29}X^{6}} + {C_{30}Y^{7}} + {C_{31}Y^{6}{X}} + {C_{32}Y^{5}X^{2}} +}} \\{{{C_{33}Y^{4}{X^{3}}} + {C_{34}Y^{3}X^{4}} + {C_{35}Y^{2}{X^{5}}} + {C_{36}{YX}^{6}} + {C_{37}{X^{7}}}}}\end{matrix} & (c)\end{matrix}$

[0144] While the shapes of the surfaces used in the examples of theinvention are expressed by the free-form surfaces using the formula (a),it is understood that similar actions and effects are obtainable even byuse of the aforesaid formulas (b) and (c).

EXAMPLE 1

[0145]FIG. 1 is a Y-Z plane schematic of Example 1 of the scanningoptical system of the invention inclusive of its optical axis (asectional schematic in the plane of the sub-scanning direction). Thisscanning optical system has a horizontal field angle of 54° and avertical field angle of 42°, and the optical deflection means is φ1 mmin size.

[0146] This scanning optical system, shown generally at 10, is designedsuch that the luminance of a light source 11 is modulated by means (notshown) for modulating the luminance of a light source depending on imagesignals for two-dimensional scanning (raster scanning) depending on theimage signals, thereby forming an image on the surface to be scanned,located in front of the image-formation optical system and at a position1 mm away therefrom, to two-dimensionally scan that surface.

[0147] Referring to an optical path for this scanning optical system 10in forward ray tracing from the light source 11 to an image plane (thesurface to be scanned, not shown), a light beam from the light source iscollimated by a condensing optical system constructed of a firsttransmitting surface 1T, a first reflecting surface 1R and a secondtransmitting surface 2T into a substantially parallel beam, which is inturn reflected and deflected at a two-dimensional scanner 12. Thereflected and deflected beam forms an image through an image-formationoptical system constructed of a third transmitting surface 3T, a secondreflecting surface 2R, a third reflecting (total reflection) surface 3Rand a fourth transmitting surface 4T on the surface to be scanned,thereby two-dimensionally scanning that surface.

[0148] For the light source, an LED, an LD or the like may be used. If aplurality of monochromatic light sources are used as shown in FIG. 2 asan example, then color displays can be achieved. In FIG. 2, forinstance, a dichroic mirror 24 for reflecting short-wavelength light,for instance, light of up to 500 nm in wavelength, is coated on a jointsurface of light-source prisms 21 and 22, each formed of a right-angleprism, and a dichroic mirror 25 for reflecting long-wavelength light,for instance, light of at least 600 nm in wavelength, is coated on ajoint surface of light-source prisms 22 and 23, each formed of aright-angle prism. Then, B light source 11 _(B), R light source 11_(R)and G light source 11 _(G) are bonded to positions conjugate toimage points on the surface to be scanned at the respective wavelengthsof the light-source prisms 21, 22 and 23, thereby eliminating theinfluence of chromatic aberrations of the scanning optical system.

[0149] With this arrangement, RGB light may be guided to the scanningoptical system 10 for color displays. At this time, the luminance of Rlight, G light, and B light is modulated by an RGB intensity modulator(not shown) for each pixel on the basis of image signals.

[0150] Some scanners may be used for the scanning means (two-dimensionalscanner) 12. However, it is noted that a micromachined scannerfabricated by making use of micromachining such as one set forth in JP-A10-20226 is best suited for use with a miniature optical system becauseof some advantages such as compactness and low power consumption.

[0151] In this case, use may be made of micromachined scanners ofvarious driving modes such as electromagnetic, electrostatic, andpiezoelectric driving modes. One example of a two-dimensionalmicromachined scanner is shown in FIG. 3 in a plan view form. In thisexample, a mirror portion 34 is joined to an intermediate framework 32with a torsion bar 33 that extends in a Y-axis direction, and thatintermediate framework 32 is joined to an outer framework 30 with atorsion bar 31 that extends in an X-axis direction, so that horizontalscanning (scanning in the X-direction) occurs due to rocking movementaround the torsion bar 33 and vertical scanning (scanning in theY-direction) takes place due to rocking movement around the torsion bar31.

[0152] In general, when a rotary polygon mirror having a plurality ofreflecting surfaces is used as a scanner, the optical system must have afunction of correction of field tilts. However, such a micromachinedscanner as shown in FIG. 3 has only one reflecting surface 34 and anyfield tilt that presents a problem is not caused for structural reasons;the optical system should not have any function of correction of fieldtilts so that it can be structurally simplified.

[0153] In this case, it is desired that the angle of incidence, θ_(S),of an axial chief ray on a reference surface for the reflecting surfacesatisfy the following formula:

θ_(S)≦45°

[0154] As the upper limit of 45° to this condition exceeds, it isdifficult to ensure a large angle of deflection and a high scanningfrequency because of an increase in the area of the reflecting surface.This holds true even for the case where the same light beam is reflectedand deflected. In this example, θ_(S)=20°.

[0155] In this example, one-way scanning is not only feasible at thedeflection angle of the sinusoidally reciprocating, but double-wayscanning is also feasible. Double-way scanning is well compatible withhigh-speed scanning because the scanning frequency of the scanning meanscan be reduced in half.

[0156] The advantages of the scanning optical system 10 according tothis example are now explained. Since the condensing optical system andimage-formation optical system are constructed of one prism member 10,the number of parts can be much reduced as compared with conventionalsystems, and so the optical system can be much reduced in size and costthan ever before. A reduced number of parts enable alignment operationsto be dispensed with, so that it is easy to ensure performance uponfabrication.

[0157] A total of four reflections occur, one at the condensing opticalsystem, two at the image-formation optical system and one at thescanner, so that the size of the optical system can be reduced by the“turn-back” effect. Since the main power of the scanning optical system10 is born by the reflecting surface, chromatic aberrations are lesslikely to occur, and even when an LD is used as the light source, theoptical performance of the scanning optical system 10 is lesssusceptible to fluctuations due to the fluctuations of the LD withwavelengths. By the combination of the second reflecting surface 2Rhaving a convex power action with the third reflecting (totalreflection) surface 3R having a concave power action, field curvaturecan be corrected all over the scanning field angle.

[0158] Due to the presence of the combined surface 2T (3T, 3R) that is acombined reflecting and transmitting surface, the number of surfacesthat form the optical system can be reduced, resulting in reductions inthe size of the condensing optical system and image-formation opticalsystem. It is then preferable to configure that surface in the form of aconcave surface because reflection occurs in the form of totalreflection.

[0159] With regard to linear scan capability and constant-speed scancapability, a general problem with a reflection type optical system ishow is the linear scan capability ensured. In this example,two-dimensional linear scan capability is ensured because the reflectingsurface has a rotationally asymmetric shape for correction of decenteredaberrations.

[0160] The deflection angle of the scan mirror 12 necessary fortwo-dimensional scanning is φx=±7.95° and φy=±3.20°. In this case, theimage-formation optical system has φ arcsine θ lens characteristics withrespect to about 65% of the sinusoidally vibrating scan mirror,two-dimensional linear, constant-speed scanning can be effected (65% ofthe amplitude of the deflection angle of the scan mirror in theX-direction, φx=±12.2°, account for the deflection angle of the mirrornecessary for scanning in the X-direction, φx=±7.95°, and 65% of theamplitude of the deflection angle of the scan mirror in the Y-direction,φy=±4.93°, account for the deflection angle of the mirror necessary forscanning in the Y-direction, φx=±3.20°).

[0161] In order to configure the image-formation optical system in theform of an f arcsine θ lens when the deflection angle of the scan mirror12 is substantially in the range defined herein, it is necessary toproduce plus distortions at the image-formation optical system. If, asin this example, the surface 4T of the image-formation optical system,which has optical power and is located nearest to the surface to bescanned, is configured in the form of an independent surface having atransmitting action alone, it is then possible to make effectivecorrection for the distortions. It is also easy to ensure the desiredfield angle.

[0162] It is here noted that if electrical correction of imagedistortions (correction of constant-speed scan capability) is carriedout to convert a non-constant-speed scan image formed by theimage-formation optical system into a constant-speed scan image, it isthen possible to make full use of the amplitude of the sinusoidallyvibrating scan mirror or a scanner with the deflection angle of a scanmirror changing linearly.

[0163] The condensing optical system has also a beam-shaping function.When the deflection means is f1 mm, the numerical aperture NA of thecondensing optical system on the light-source side is 0.16 in theX-direction and 0.19 in the Y-direction.

[0164] In this example, a two-dimensional image is formed bytwo-dimensional scanning of point sources 11 of light. However, it isacceptable to one-dimensionally scan a linear array of light sources.

[0165] In this example, the scanning optical system is designed on theassumption that the size of the scanner in the X-direction is equal tothat in the Y-direction. In order to make the resolving power of thescanner in the X-direction equal to that in the Y-direction on the sideof the surface to be scanned or for other purposes, however, it isacceptable that the size of the scanner 12 in the X-direction is notequal to that in the Y-direction.

EXAMPLE 2

[0166] The scanning optical system of this example is shown in FIG. 4similar to FIG. 1, and has a horizontal field angle of 54° and avertical field angle of 42°.

[0167] This scanning optical system 10 is constructed as in Example 1.To be specific, the luminance of a light source 11 is modulated by means(not shown) for modulating the luminance of a light source depending onimage signals for two-dimensional scanning (raster scanning) dependingon the image signals, thereby forming an image on the surface to bescanned, located in front of the image-formation optical system and at aposition 1 mm away therefrom, to two-dimensionally scan that surface.

[0168] Referring to an optical path for this scanning optical system 10in forward ray tracing from the light source 11 to an image plane (thesurface to be scanned, not shown), a light beam from the light source iscollimated by a condensing optical system constructed of a firsttransmitting surface 1T, a first reflecting surface 1R and a secondtransmitting surface 2T into a substantially parallel beam, which is inturn reflected and deflected at a two-dimensional scanner 12. Thereflected and deflected beam forms an image through an image-formationoptical system constructed of a third transmitting surface 3T, a secondreflecting surface 2R, a third reflecting (total reflection) surface 3Rand a fourth transmitting surface 4T on the surface to be scanned,thereby two-dimensionally scanning that surface.

[0169] In this example, the f arcsine θ lens characteristics are moreimproved than that in Example 1. The f arcsine θ lens characteristicsare achieved for the sinusoidally vibrating scan mirror 12 at about 70%of the amplitude of the deflection angle of the scan mirror in both theX-direction and the Y-direction.

[0170] It is noted that if lenses, etc. are added between the prism 10where distortions are easy to control and the surface to be scanned, thef arcsine θ lens characteristics can then be even more improved.

EXAMPLE 3

[0171] The scanning optical system of this example is shown in FIG. 5similar to FIG. 1, and has a horizontal field angle of 54° and avertical field angle of 42° while the optical deflection means is φ1 mmin size.

[0172] This scanning optical system 10 is constructed as in Example 1 or2. To be specific, the luminance of a light source 11 is modulated bymeans (not shown) for modulating the luminance of a light sourcedepending on image signals for two-dimensional scanning (rasterscanning) depending on the image signals, thereby forming an image onthe surface to be scanned, located in front of the image-formationoptical system and at a position 1 mm away therefrom, totwo-dimensionally scan that surface.

[0173] Referring to an optical path for this scanning optical system 10in forward ray tracing from the light source 11 to an image plane (thesurface to be scanned, not shown), a light beam from the light source iscollimated by a condensing optical system constructed of a firsttransmitting surface 1T, a first reflecting surface 1R and a secondtransmitting surface 2T into a substantially parallel beam, which is inturn reflected and deflected at a two-dimensional scanner 12. Thereflected and deflected beam forms an image through an image-formationoptical system constructed of a third transmitting surface 3T, a secondreflecting surface 2R, a third reflecting (total reflection) surface 3Rand a fourth transmitting surface 4T on the surface to be scanned,thereby two-dimensionally scanning that surface.

[0174] In this example, when the deflection means 12 with a linearlychanging angle of deflection such as a rotary polygon mirror is used,the image-formation optical system is configured in such an fθ lens (atwo-dimensional fθ lens with respect to the main scanning direction inthe X-direction and the sub-scanning direction in the Y-direction) formthat the surface to be scanned is scanned at constant speed.

EXAMPLE 4

[0175] The scanning optical system of this example is shown in FIG. 6similar to FIG. 1, and has a horizontal field angle of 47° and avertical field angle of 36° while the optical deflection means is φ1.1mm in size.

[0176] This scanning optical system 10 is constructed as in Example 1, 2or 3 with the exception that a DOE (diffractive optical element) 13 isinterposed between a prism 10 and a scanner 12. To be specific, theluminance of a light source 11 is modulated by means (not shown) formodulating the luminance of a light source depending on image signalsfor two-dimensional scanning (raster scanning) depending on the imagesignals, thereby forming an image on the surface to be scanned, locatedin front of the image-formation optical system and at a position 1 mmaway therefrom, to two-dimensionally scan that surface.

[0177] Referring to an optical path for this scanning optical system 10in forward ray tracing from the light source 11 to an image plane (thesurface to be scanned, not shown), a light beam from the light source iscollimated by a condensing optical system constructed of a firsttransmitting surface 1T, a first reflecting surface 1R, a secondtransmitting surface 2T and DOE 13 with a diffracting surface 14 locatedin opposition to the scanner 12 into a substantially parallel beam,which is in turn reflected and deflected at a two-dimensional scanner12. The reflected and deflected beam forms an image through animage-formation optical system constructed of DOE 13 with thediffracting surface 14 facing the scanner 12, a third transmittingsurface 3T, a second reflecting surface 2R, a third reflecting (totalreflection) surface 3R and a fourth transmitting surface 4T on thesurface to be scanned, thereby two-dimensionally scanning that surface.

[0178] In this example, the DOE 13 is interposed between the prism 10and the scanner 12 to correct the scanning optical system for chromaticaberrations. The DOE 13 works both on the beam leaving the condensingoptical system and directing to the scanner 12 and on the beam incidentfrom the scanner 12 on the image-formation optical system.

[0179] It is noted that when a micromachined scanner is used as thetwo-dimensional scanner 12, it may be made integral with the scanner 12.For instance, a substrate with ODE 13 formed thereon may be used as aprotecting or sealing member for the scanner 12.

EXAMPLE 5

[0180] The scanning optical system of this example is shown in FIG. 7similar to FIG. 1. This scanning optical system 10 is constructed as inExample 1, 2 or 3 with the exception that a DOE 13 is interposed betweena light source 11 and a prism 10. To be specific, the luminance of alight source 11 is modulated by means (not shown) for modulating theluminance of a light source depending on image signals fortwo-dimensional scanning (raster scanning) depending on the imagesignals, thereby forming an image on the surface to be scanned, locatedin front of the image-formation optical system and at a position 1 mmaway therefrom, to two-dimensionally scan that surface.

[0181] Referring to an optical path for this scanning optical system 10in forward ray tracing from the light source 11 to an image plane (thesurface to be scanned, not shown), a light beam from the light source iscollimated by a condensing optical system constructed of DOE 13 with adiffracting surface 14 in opposition to the prism 10, a firsttransmitting surface 1T, a first reflecting surface 1R and a secondtransmitting surface 2T into a substantially parallel beam, which is inturn reflected and deflected at a two-dimensional scanner 12. Thereflected and deflected beam forms an image through an image-formationoptical system constructed of a third transmitting surface 3T, a secondreflecting surface 2R, a third reflecting (total reflection) surface 3Rand a fourth transmitting surface 4T on the surface to be scanned,thereby two-dimensionally scanning that surface.

[0182] In this example, the DOE 13 is interposed between the lightsource 11 and the prism 10 to correct the scanning optical system forchromatic aberrations.

EXAMPLE 6

[0183] The scanning optical system of this example is shown in FIG. 8similar to FIG. 1. This is a one-dimensional scanning optical systemhaving a horizontal field angle of 82°, and comprising a scanner of φ2.6mm in size.

[0184] This scanning optical system 10 is substantially constructed asin Example 1. To be specific, the luminance of a light source 11 ismodulated by means (not shown) for modulating the luminance of a lightsource depending on image signals for one-dimensional scanning in thehorizontal (X) direction depending on the image signals, thereby formingan image on the surface to be scanned, located in front of the firstsurface 4T going back to a non-decentered state and at a position 1 mmaway therefrom, to two-dimensionally scan that surface.

[0185] Referring to an optical path for this scanning optical system 10in forward ray tracing from the light source 11 to an image plane (thesurface to be scanned, not shown), a light beam from the light source iscollimated by a condensing optical system constructed of a firsttransmitting surface 1T, a first reflecting surface 1R and a secondtransmitting surface 2T into a substantially parallel beam, which is inturn reflected and deflected at a two-dimensional scanner 12. Thereflected and deflected beam forms an image through an image-formationoptical system constructed of a third transmitting surface 3T, a secondreflecting surface 2R, a third reflecting (total reflection) surface 3Rand a fourth transmitting surface 4T on the surface to be scanned,thereby one-dimensionally scanning that surface.

[0186] In this example, the main scanning (X) direction has f arcsine θlens characteristics at 95% of the amplitude of the deflection angle ofthe scanner with the deflection angle changing sinusoidally.

[0187] Set out below are the constitutional parameters (lens data) ofExamples 1 to 6. In the following data, “FFS”, “RS” and “DOE” stand fora free-form surface, a reflecting surface and a diffracting surface,respectively. It is noted that the scanner is located at a stop surfaceand the light source is positioned on an image plane.

EXAMPLE 1

[0188] Re- Surface Radius of Surface Displacement fractive Abbe's No.curvature separation and tilt index No. Object ∞ 1000.00 plane 1 F F S{circle over (1)} (1) 1.5254 56.3 2 F F S {circle over (2)}(RS) (2)1.5254 56.3 3 F F S {circle over (3)}(RS) (3) 1.5254 56.3 4 F F S{circle over (2)} (2) 5 ∞ (Stop) (4) 6 F F S {circle over (2)} (2)1.5254 56.3 7 F F S {circle over (4)}(RS) (5) 1.5254 56.3 8 F F S{circle over (5)} (6) Image ∞ (7) plane F F S 1 C₄ −2.5779 × 10⁻² C₆−1.2030 × 10⁻¹ C₈ −1.1075 × 10⁻² C₁₀ −1.8153 × 10⁻² C₁₁   2.5232 × 10⁻⁴C₁₃   7.6132 × 10⁻³ C₁₅   3.4561 × 10⁻³ C₁₇   1.9873 × 10⁻⁴ C₁₉   2.2454× 10⁻⁴ C₂₁   6.3462 × 10⁻⁴ C₂₂   1.9509 × 10⁻⁶ C₂₄ −1.1858 × 10⁻⁴ C₂₆−2.2337 × 10⁻⁴ C₂₈ −1.0408 × 10⁻⁴ F F S 2 C₄   7.7922 × 10⁻⁴ C₆   7.7495× 10⁻³ C₈   3.7699 × 10⁻³ C₁₀ −2.3003 × 10⁻³ C₁₁   3.8795 × 10⁻⁴ C₁₃  2.1619 × 10⁻³ C₁₅   2.1746 × 10⁻⁴ C₁₇   3.0215 × 10⁻⁴ C₁₉   4.7146 ×10⁻⁴ C₂₁   5.4788 × 10⁻⁵ C₂₂ −2.2446 × 10⁻⁶ C₂₄   6.4487 × 10⁻⁵ C₂₆  6.0274 × 10⁻⁵ C₂₈   7.6776 × 10⁻⁶ F F S 3 C₄ −2.2371 × 10⁻² C₆  1.1690 × 10⁻² C₈   7.2963 × 10⁻⁴ C₁₀   6.5994 × 10⁻⁴ C₁₁   7.9455 ×10⁻⁴ C₁₃   1.1221 × 10⁻³ C₁₅ −1.4706 × 10⁻⁵ C₁₇ −9.7208 × 10⁻⁴ C₁₉−6.3757 × 10⁻⁴ C₂₁ −3.9919 × 10⁻⁵ C₂₂ −1.0684 × 10⁻⁴ C₂₄   3.3217 × 10⁻⁴C₂₆   1.1244 × 10⁻⁴ C₂₈ −2.2822 × 10⁻⁶ F F S 4 C₄   3.3846 × 10⁻² C₆  2.9857 × 10⁻² C₈ −9.7283 × 10⁻³ C₁₀ −5.0879 × 10⁻³ C₁₁ −2.5332 × 10⁻³C₁₃ −4.6775 × 10⁻⁴ C₁₅ −1.1206 × 10⁻³ C₁₇   2.2389 × 10⁻³ C₁₉   1.5076 ×10⁻³ C₂₁ −2.6497 × 10⁻⁴ C₂₂   8.4446 × 10⁻⁴ C₂₄   1.6456 × 10⁻³ C₂₆  4.9022 × 10⁻⁴ C₂₈ −2.7959 × 10⁻⁵ F F S 5 C₄ −5.0621 × 10⁻¹ C₆ −1.9566× 10⁻¹ C₈ −2.5991 × 10⁻¹ C₁₀ −8.7768 × 10⁻³ C₁₁   3.1809 × 10⁻¹ C₁₃  4.2980 × 10⁻¹ C₁₅   2.6434 × 10⁻² Displacement and tilt(1) X 0.00 Y−1.50 Z 0.00 α 0.00 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.62Z 4.94 α −45.15 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 2.80 Z2.00 α −73.15 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y −1.00 Z.66 α −52.18 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 2.66 Z 1.68α −66.23 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y −3.05 Z 0.58 α−79.91 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −3.98 Z 0.78 α−100.29 β 0.00 γ 0.00

EXAMPLE 2

[0189] Re- Surface Radius of Surface Displacement fractive Abbe's No.curvature separation and tilt index No. Object ∞ 1000.00 plane 1 F F S{circle over (1)} (1) 1.5254 56.3 2 F F S {circle over (2)}(RS) (2)1.5254 56.3 3 F F S {circle over (3)}(RS) (3) 1.5254 56.3 4 F F S{circle over (2)} (2) 5 ∞ (Stop) (4) 6 F F S {circle over (2)} (2)1.5254 56.3 7 F F S {circle over (4)}(RS) (5) 1.5254 56.3 8 F F S{circle over (5)} (6) Image ∞ (7) plane F F S 1 C₄   1.2830 × 10⁻² C₆−1.0765 × 10⁻¹ C₈ −6.8597 × 10⁻³ C₁₀ −7.3302 × 10⁻³ C₁₁   6.8784 × 10⁻⁵C₁₃   2.0958 × 10⁻³ C₁₅   4.2746 × 10⁻³ C₁₇ −1.4056 × 10⁻⁵ C₁₉   2.1878× 10⁻⁴ C₂₁ −5.6130 × 10⁻⁴ C₂₂   1.2335 × 10⁻⁶ C₂₄ −8.3175 × 10⁻⁶ C₂₆−7.0819 × 10⁻⁵ C₂₈   3.5824 × 10⁻⁵ F F S 2 C₄ −1.2602 × 10⁻³ C₆   6.5870× 10⁻³ C₈   8.6539 × 10⁻⁴ C₁₀ −1.4889 × 10⁻³ C₁₁   9.7681 × 10⁻⁵ C₁₃  6.7863 × 10⁻⁴ C₁₅   2.6351 × 10⁻⁵ C₁₇ −7.9227 × 10⁻⁶ C₁₉   1.2881 ×10⁻⁴ C₂₁   4.1327 × 10⁻⁵ C₂₂ −1.3352 × 10⁻⁶ C₂₄ −2.8331 × 10⁻⁶ C₂₆  1.2199 × 10⁻⁵ C₂₈   5.7971 × 10⁻⁶ F F S 3 C₄ −1.9853 × 10⁻² C₆  1.2833 × 10⁻² C₈ −5.2848 × 10⁻⁴ C₁₀   3.7366 × 10⁻⁴ C₁₁   2.2434 ×10⁻⁴ C₁₃   6.4856 × 10⁻⁴ C₁₅   1.9609 × 10⁻⁶ C₁₇   2.1708 × 10⁻⁵ C₁₉−3.0213 × 10⁻⁴ C₂₁ −1.6660 × 10⁻⁵ C₂₂ −3.2798 × 10⁻⁵ C₂₄ −2.4481 × 10⁻⁶C₂₆   4.3731 × 10⁻⁵ C₂₈ −3.4736 × 10⁻⁶ F F S 4 C₄   3.5143 × 10⁻² C₆  2.9244 × 10⁻² C₈ −1.0733 × 10⁻² C₁₀ −4.6492 × 10⁻³ C₁₁ −3.7851 × 10⁻³C₁₃ −4.4587 × 10⁻³ C₁₅ −1.1223 × 10⁻³ C₁₇ −1.5160 × 10⁻³ C₁₉ −1.2923 ×10⁻³ C₂₁ −3.0248 × 10⁻⁴ C₂₂ −4.5680 × 10⁻⁴ C₂₄ −1.2579 × 10⁻⁴ C₂₆−1.7631 × 10⁻⁴ C₂₈ −3.7567 × 10⁻⁵ F F S 5 C₄ −4.7149 × 10⁻¹ C₆ −1.8302 ×10⁻¹ C₈ −1.5918 × 10⁻¹ C₁₀ −1.0259 × 10⁻² C₁₁   1.8967 × 10⁻¹ C₁₃  2.7011 × 10⁻¹ C₁₅   2.3839 × 10⁻² Displacement and tilt(1) X 0.00 Y−1.50 Z 0.00 α 0.00 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.91Z 4.98 α −46.60 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 2.80 Z1.83 α −73.91 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y −1.00 Z5.62 α −50.77 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 2.64 Z1.67 α −65.89 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y −3.05 Z0.60 α −79.70 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −3.96 Z0.83 α −98.37 β 0.00 γ 0.00

EXAMPLE 3

[0190] Re- Surface Radius of Surface Displacement fractive Abbe's No.curvature separation and tilt index No. Object ∞ 1000.00 plane 1 F F S{circle over (1)} (1) 1.5254 56.3 2 F F S {circle over (2)}(RS) (2)1.5254 56.3 3 F F S {circle over (3)}(RS) (3) 1.5254 56.3 4 F F S{circle over (2)} (2) 5 ∞ (Stop) (4) 6 F F S {circle over (2)} (2)1.5254 56.3 7 F F S {circle over (4)}(RS) (5) 1.5254 56.3 8 F F S{circle over (5)} (6) Image ∞ (7) plane F F S 1 C₄   2.0048 × 10⁻³ C₆−6.5253 × 10⁻² C₈ −2.1891 × 10⁻³ C₁₀ −5.2349 × 10⁻² C₁₁   4.3385 × 10⁻⁴C₁₃   2.5336 × 10⁻³ C₁₅   8.2781 × 10⁻³ C₁₇ −2.3112 × 10⁻⁵ C₁₉ −4.8161 ×10⁻⁴ C₂₁   3.6053 × 10⁻³ C₂₂ −5.0443 × 10⁻⁶ C₂₄ −1.0024 × 10⁻⁵ C₂₆  4.9410 × 10⁻⁵ C₂₈ −8.4784 × 10⁻⁴ F F S 2 C₄   9.3276 × 10⁻³ C₆  1.2305 × 10⁻² C₈   3.3701 × 10⁻³ C₁₀   6.2067 × 10⁻⁴ C₁₁ −2.6194 ×10⁻⁴ C₁₃   5.5084 × 10⁻⁴ C₁₅ −1.7807 × 10⁻⁴ C₁₇ −9.2688 × 10⁻⁵ C₁₉  2.3851 × 10⁻⁴ C₂₁ −6.1960 × 10⁻⁵ C₂₂   1.1482 × 10⁻⁷ C₂₄ −7.7827 ×10⁻⁶ C₂₆   4.1871 × 10⁻⁵ C₂₈   8.9363 × 10⁻⁶ F F S 3 C₄ −1.1936 × 10⁻²C₆   1.5613 × 10⁻² C₈   9.8371 × 10⁻⁴ C₁₀ −3.2433 × 10⁻⁴ C₁₁ −5.0154 ×10⁻⁴ C₁₃   3.1318 × 10⁻³ C₁₅ −6.5157 × 10⁻⁶ C₁₇ −2.8893 × 10⁻⁴ C₁₉−1.1561 × 10⁻³ C₂₁   3.2209 × 10⁻⁵ C₂₂   3.9739 × 10⁻⁵ C₂₄   7.0920 ×10⁻⁵ C₂₆   1.2812 × 10⁻⁴ C₂₈ −3.3532 × 10⁻⁶ F F S 4 C₄   2.1168 × 10⁻²C₆   3.1444 × 10⁻² C₈ −1.2773 × 10⁻² C₁₀ −4.9250 × 10⁻³ C₁₁   1.8772 ×10⁻⁴ C₁₃ −9.2233 × 10⁻⁴ C₁₅ −1.2437 × 10⁻³ C₁₇   2.5286 × 10⁻² C₁₉  4.5186 × 10⁻³ C₂₁ −3.0342 × 10⁻⁴ C₂₂   1.6796 × 10⁻² C₂₄   1.3450 ×10⁻² C₂₆   1.6931 × 10⁻³ C₂₈ −2.7316 × 10⁻⁵ F F S 5 C₄ −7.6734 × 10⁻¹ C₆−2.4281 × 10⁻¹ C₈   1.0370 × 10⁻² C₁₀ −3.9036 × 10⁻² C₁₁   5.0781 × 10⁻¹C₁₃   3.5355 × 10⁻¹ C₁₅   5.0029 × 10⁻² Displacement and tilt(1) X 0.00Y −1.50 Z 0.00 α 0.00 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y1.00 Z 5.00 α −44.98 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y2.76 Z 1.84 α −75.17 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y−1.00 Z 4.95 α −60.82 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y2.60 Z 1.61 α −67.95 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y−3.01 Z 0.75 α −83.98 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y−3.97 Z 0.94 α −98.76 β 0.00 γ 0.00

EXAMPLE 4

[0191] Re- Surface Radius of Surface Displacement fractive Abbe's No.curvature separation and tilt index No. Object ∞ 1000.00 plane  1 F F S{circle over (1)} (1)  1.5254 56.3  2 F F S {circle over (2)}(RS) (2) 1.5254 56.3  3 F F S {circle over (3)}(RS) (3)  1.5254 56.3  4 F F S{circle over (2)} (2)   5 ∞ (4)  1.5254 56.3  6 ∞ (5)  1001.00 −3.45  7F F S {circle over (4)}(DOE) (6)   8 ∞ (Stop) (7)   9 F F S {circle over(4)}(DOE) (6)  1001.00 −3.45 10 ∞ (5)  1.5254 56.3 11 ∞ (4)  12 F F S{circle over (2)} (2)  1.5254 56.3 13 F F S {circle over (5)}(RS) (8) 1.5254 56.3 14 F F S {circle over (6)} (9)  Image ∞ (10) plane F F S 1C₄ −5.1153 × 10⁻³ C₆   1.3925 × 10⁻² C₈ −7.3841 × 10⁻³ C₁₀ −1.1875 ×10⁻² C₁₁ −7.5853 × 10⁻⁵ C₁₃   1.2571 × 10⁻³ C₁₅   1.6283 × 10⁻³ C₁₇  5.6232 × 10⁻⁵ C₁₉   2.0110 × 10⁻⁴ C₂₁ −4.8468 × 10⁻⁴ C₂₂   9.0171 ×10⁻⁷ C₂₄ −1.1171 × 10⁻⁵ C₂₆ −2.0169 × 10⁻⁵ C₂₈   6.5369 × 10⁻⁵ F F S 2C₄   1.4932 × 10⁻² C₆ −1.9540 × 10⁻³ C₈   4.4504 × 10⁻³ C₁₀ −2.4909 ×10⁻³ C₁₁   6.1319 × 10⁻⁵ C₁₃   8.8673 × 10⁻⁴ C₁₅ −2.8323 × 10⁻⁴ C₁₇  7.3968 × 10⁻⁶ C₁₉   4.5864 × 10⁻⁵ C₂₁ −2.3171 × 10⁻⁶ C₂₂   5.2961 ×10⁻⁸ C₂₄ −4.5057 × 10⁻⁷ C₂₆ −2.4771 × 10⁻⁶ C₂₈   1.8540 × 10⁻⁶ F F S 3C₄ −2.9939 × 10⁻³ C₆ −1.1909 × 10⁻² C₈   1.2713 × 10⁻² C₁₀ −9.0051 ×10⁻⁴ C₁₁ −1.3110 × 10⁻⁴ C₁₃ −4.5404 × 10⁻³ C₁₅   5.2681 × 10⁻⁴ C₁₇  4.0962 × 10⁻⁵ C₁₉   1.1500 × 10⁻³ C₂₁   7.2718 × 10⁻⁵ C₂₂ −1.2274 ×10⁻⁶ C₂₄ −7.7261 × 10⁻⁶ C₂₆ −1.0427 × 10⁻⁴ C₂₈ −2.2896 × 10⁻⁵ F F S 4 C₄−6.1596 × 10⁻⁷ C₆   3.4175 × 10⁻⁶ C₈ −3.2523 × 10⁻⁶ C₁₀ −9.3052 × 10⁻⁷C₁₁ −4.0783 × 10⁻⁷ C₁₃ −5.9660 × 10⁻⁶ C₁₅ −2.3863 × 10⁻⁶ C₁₇ −2.8541 ×10⁻⁷ C₁₉ −1.9365 × 10⁻⁶ C₂₁ −5.8348 × 10⁻⁷ F F S 5 C₄   2.3949 × 10⁻² C₆  3.3604 × 10⁻² C₈ −5.7943 × 10⁻⁴ C₁₀   9.6778 × 10⁻⁴ C₁₁ −8.4834 × 10⁻⁴C₁₃ −4.2016 × 10⁻³ C₁₅   2.3946 × 10⁻⁴ C₁₇ −3.0987 × 10⁻³ C₁₉   2.4318 ×10⁻³ C₂₁ −4.9242 × 10⁻⁴ C₂₂   7.0481 × 10⁻⁴ C₂₄ −2.4279 × 10⁻³ C₂₆−1.3842 × 10⁻³ C₂₈   1.6279 × 10⁻⁴ F F S 6 C₄ −1.0093 C₆ −2.4736 × 10⁻¹C₈ −1.4848 C₁₀ −1.3260 × 10⁻² C₁₁   2.9043 × 10⁻¹ C₁₃ −8.9842 × 10⁻¹ C₁₅  5.2718 × 10⁻² Displacement and tilt(1) X 0.00 Y −1.50 Z 0.00 α 0.00 β0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 1.12 Z 5.50 α −50.08 β0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 3.00 Z 2.00 α −87.13 β0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y 0.07 Z 5.03 α −50.80 β0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 0.11 Z 5.46 α −50.799815 β0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y 0.57 Z 6.03 α −50.799876 β0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −0.88 Z 5.60 α −59.62 β0.00 γ 0.00 Displacement and tilt(8) X 0.00 Y 2.60 Z 1.00 α −67.35 β0.00 γ 0.00 Displacement and tilt(9) X 0.00 Y −3.00 Z 1.11 α −107.34 β0.00 γ 0.00 Displacement and tilt(10) X 0.00 Y −3.84 Z 0.84 α −83.74 β0.00 γ 0.00

EXAMPLE 5

[0192] Re- Surface Radius of Surface Displacement fractive Abbe's No.curvature separation and tilt index No. Object ∞ 1000.00 plane  1 F F S{circle over (1)} (1) 1.5254 56.3  2 F F S {circle over (2)}(RS) (2)1.5254 56.3  3 F F S {circle over (3)}(RS) (3) 1.5254 56.3  4 F F S{circle over (2)} (2)  5 ∞ (Stop) (4)  6 F F S {circle over (2)} (2)1.5254 56.3  7 F F S {circle over (4)}(RS) (5) 1.5254 56.3  8 F F S{circle over (5)} (6)  9 F F S {circle over (6)}(DOE) (7) 1001.00 −3.4510 ∞ (8) 1.5254 56.3 11 ∞ (9) Image ∞  (10) plane F F S 1 C₄   2.7110 ×10⁻³ C₆ −4.1822 × 10⁻² C₈ −8.3156 × 10⁻³ C₁₀ −2.6287 × 10⁻² C₁₁ −8.1512× 10⁻⁶ C₁₃   4.1432 × 10⁻³ C₁₅ −6.5747 × 10⁻⁴ C₁₇   2.9008 × 10⁻⁶ C₁₉  1.9125 × 10⁻⁴ C₂₁   2.6876 × 10⁻⁴ C₂₂ −8.9097 × 10⁻⁶ C₂₄ −7.0018 ×10⁻⁵ C₂₆   2.5234 × 10⁻⁶ C₂₈ −3.2872 × 10⁻⁵ F F S 2 C₄ −6.3232 × 10⁻³ C₆  6.0261 × 10⁻³ C₈ −3.2915 × 10⁻⁴ C₁₀ −4.4498 × 10⁻³ C₁₁ −1.7090 × 10⁻⁵C₁₃   1.7254 × 10⁻³ C₁₅   7.9047 × 10⁻⁴ C₁₇ −1.5791 × 10⁻⁴ C₁₉   3.8668× 10⁻⁴ C₂₁   6.0282 × 10⁻⁵ C₂₂ −1.8162 × 10⁻⁵ C₂₄ −3.4431 × 10⁻⁵ C₂₆  5.1730 × 10⁻⁵ C₂₈   9.2060 × 10⁻⁷ F F S 3 C₄ −1.6315 × 10⁻² C₆  1.2307 × 10⁻² C₈ −1.8756 × 10⁻³ C₁₀   6.2970 × 10⁻⁴ C₁₁   9.5379 ×10⁻⁵ C₁₃   1.3103 × 10⁻³ C₁₅ −1.1967 × 10⁻⁴ C₁₇ −2.8876 × 10⁻⁵ C₁₉−8.6467 × 10⁻⁴ C₂₁ −5.1857 × 10⁻⁵ C₂₂ −8.1252 × 10⁻⁵ C₂₄   1.2131 × 10⁻⁴C₂₆   1.3258 × 10⁻⁴ C₂₈   6.3820 × 10⁻⁶ F F S 4 C₄   2.9891 × 10⁻² C₆  3.0951 × 10⁻² C₈ −9.3571 × 10⁻³ C₁₀ −5.2875 × 10⁻³ C₁₁ −5.1673 × 10⁻³C₁₃ −5.1317 × 10⁻⁴ C₁₅ −1.1087 × 10⁻³ C₁₇   2.6635 × 10⁻³ C₁₉   1.8630 ×10⁻³ C₂₁ −2.6829 × 10⁻⁴ C₂₂   3.4886 × 10⁻³ C₂₄   1.8096 × 10⁻³ C₂₆  8.2598 × 10⁻⁴ C₂₈ −2.4770 × 10⁻⁵ F F S 5 C₄ −6.8396 × 10⁻¹ C₆ −2.0892× 10⁻¹ C₈ −1.7517 × 10⁻¹ C₁₀ −1.2761 × 10⁻² C₁₁   4.5728 × 10⁻¹ C₁₃  5.5687 × 10⁻¹ C₁₅   3.3352 × 10⁻² F F S 6 C₄   1.0559 × 10⁻⁴ C₆  3.9513 × 10⁻⁵ C₈   1.8847 × 10⁻⁴ C₁₀   1.6785 × 10⁻⁴ C₁₁ −2.8750 ×10⁻⁴ C₁₃ −4.6702 × 10⁻³ C₁₅   3.1902 × 10⁻⁵ C₁₇   4.4625 × 10⁻³ C₁₉  2.0071 × 10⁻² C₂₁ −4.6995 × 10⁻⁵ Displacement and tilt(1) X 0.00 Y−1.50 Z 0.00 α 0.00 β 0.00 γ 0.00 Displacement and tilt(2) X 0.00 Y 0.34Z 4.92 α −50.44 β 0.00 γ 0.00 Displacement and tilt(3) X 0.00 Y 2.80 Z1.89 α −74.09 β 0.00 γ 0.00 Displacement and tilt(4) X 0.00 Y −0.82 Z5.86 α −46.70 β 0.00 γ 0.00 Displacement and tilt(5) X 0.00 Y 2.64 Z1.68 α −66.07 β 0.00 γ 0.00 Displacement and tilt(6) X 0.00 Y −3.05 Z0.54 α −81.32 β 0.00 γ 0.00 Displacement and tilt(7) X 0.00 Y −3.34 Z0.76 α −99.9998651 β 0. 00 γ 0.00 Displacement and tilt(8) X 0.00 Y−3.36 Z 0.83 α −100.00 β 0.00 γ 0.00 Displacement and tilt(9) X 0.00 Y−3.79 Z 0.66 α −100.00 β 0.00 γ 0.00 Displacement and tilt(10) X 0.00 Y−4.00 Z 0.71 α −101.17 β 0.00 γ 0.00

EXAMPLE 6

[0193] Re- Surface Radius of Surface Displacement fractive Abbe's No.curvature separation and tilt index No. Object ∞ 10.00 plane 1 F F S{circle over (1)} (1) 1.5254 56.3 2 F F S {circle over (2)}(RS) (2)1.5254 56.3 3 F F S {circle over (3)}(RS) (3) 1.5254 56.3 4 F F S{circle over (2)} (2) 5 ∞ (Stop) (4) 6 F F S {circle over (2)} (2)1.5254 56.3 7 F F S {circle over (4)}(RS) (5) 1.5254 56.3 8 F F S{circle over (5)} (6) Image ∞ (7) plane F F S 1 C₄ −1.4579 × 10⁻² C₆−1.0257 × 10⁻¹ C₈ −9.2040 × 10⁻⁴ C₁₀ −1.0489 × 10⁻² C₁₁ −9.9035 × 10⁻⁵C₁₃   5.9168 × 10⁻³ C₁₅   4.8469 × 10⁻³ C₁₇ −8.7514 × 10⁻⁶ C₁₉   1.2191× 10⁻³ C₂₁ −9.9794 × 10⁻⁴ F F S 2 C₄   1.3960 × 10⁻² C₆   1.2346 × 10⁻²C₈   2.4723 × 10⁻³ C₁₀   1.0147 × 10⁻⁴ C₁₁ −1.6176 × 10⁻⁴ C₁₃   8.1886 ×10⁻⁴ C₁₅   2.0947 × 10⁻⁵ C₁₇ −1.7977 × 10⁻⁴ C₁₉   4.1117 × 10⁻⁵ C₂₁−1.1700 × 10⁻⁴ F F S 3 C₄   9.3942 × 10⁻³ C₆   1.7229 × 10⁻² C₈   2.3970× 10⁻³ C₁₀   3.5790 × 10⁻⁵ C₁₁   2.9999 × 10⁻⁴ C₁₃   3.8118 × 10⁻⁵ C₁₅−1.6410 × 10⁻⁴ C₁₇ −1.3152 × 10⁻⁴ C₁₉ −1.6937 × 10⁻⁵ C₂₁ −5.3560 × 10⁻⁶F F S 4 C₄   4.6653 × 10⁻² C₆   3.4104 × 10⁻² C₈ −1.6228 × 10⁻² C₁₀−7.5431 × 10⁻³ C₁₁ −3.0449 × 10⁻³ C₁₃ −1.8865 × 10⁻³ C₁₅   7.5485 × 10⁻⁴C₁₇   1.5596 × 10⁻³ C₁₉   1.3141 × 10⁻³ C₂₁   4.0652 × 10⁻⁴ F F S 5 C₄−3.3176 × 10⁻¹ C₆ −1.4184 × 10⁻¹ C₈   2.4167 × 10⁻¹ C₁₀   1.2728 × 10⁻¹C₁₁   8.8749 × 10⁻² C₁₃ −1.0491 × 10⁻¹ C₁₅ −6.7796 × 10⁻² Displacementand tilt(1) X 0.00 Y .58 Z 0.00 α 0.00 β 0.00 γ 0.00 Displacement andtilt(2) X 0.00 Y 1.20 Z 4.13 α −47.90 β 0.00 γ 0.00 Displacement andtilt(3) X 0.00 Y 1.40 Z 0.70 α −68.85 β 0.00 γ 0.00 Displacement andtilt(4) X 0.00 Y −1.00 Z 4.40 α −48.05 β 0.00 γ 0.00 Displacement andtilt(5) X 0.00 Y 1.78 Z 1.68 α −65.43 β 0.00 γ 0.00 Displacement andtilt(6) X 0.00 Y −1.39 Z 1.33 α −61.77 β 0.00 γ 0.00 Displacement andtilt(7) X 0.00 Y −2.47 Z 1.04 α −97.55 β 0.00 γ 0.00

[0194] The values of conditions (1) and (2) in Examples 1 through 6 aregiven below. It is understood that when upper and lower marginal lightrays are asymmetric with respect to a chief light ray, NAy (NA2) isfound by averaging both. Ex. (A) (B) (C) (D) (E) (F) (G) (H) 1 ±7.95±3.20 0.59 0.30 0.52 0.16 0.19 1.20 2 ±10.6 ±4.42 0.79 0.42 0.54 0.150.19 1.28 3 ±12.6 ±4.87 0.93 0.46 0.50 0.25 0.26 1.02 4 ±12.2 ±6.10 1.040.68 0.65 0.13 0.18 1.41 5 ±10.0 ±2.45 0.74 0.23 0.32 0.14 0.26 1.91 6±20.5 0.22 0.37 1.73

[0195] While Examples 1 to 6 of the scanning optical system areconstructed using the free-form surfaces conforming to the aforesaiddefining formula (a), it is understood that the optical system of theinvention may be constructed even with curved surfaces that meet otherdefining formulae.

[0196] While the scanning optical system of the present invention hasbeen described with reference to several embodiments, it is understoodthat the invention is not limited thereto and so many modificationsthereto may be possible.

[0197] According to the present invention wherein the scanning opticalsystem is constructed mainly with a prism member including a reflectingaction, the number of parts that form the scanning optical system can bereduced with size reductions.

What we claim is:
 1. A scanning optical system comprising: opticaldeflection means for deflecting light from a light source to scan thesurface to be scanned, and an image-formation optical system forfocusing the light deflected by said optical deflection means on thesurface to be scanned, thereby forming an image thereon, characterizedin that: said image-formation optical system comprises an optical memberwherein a surface thereof having optical power and located nearest tothe surface to be scanned has a transmission function alone, and saidoptical member comprises two or more reflecting surfaces, each of whichhas optical power and includes at least one rotationally asymmetricsurface decentered with respect to an axial chief ray.
 2. The scanningoptical system according to claim 1, characterized in that said opticalmember is configured as a prism member.
 3. The scanning optical systemaccording to claim 1, characterized in that said optical member has atleast one surface having a function of transmitting light and a functionof reflecting light.
 4. A scanning optical system comprising: acondensing optical system for collimating a light beam from a lightsource into a substantially parallel beam, an optical deflection meansfor deflecting light emerging from said condensing optical system forscanning the surface to be scanned, and an image-formation opticalsystem for focusing light deflected by said optical deflection means onthe surface to be scanned, thereby forming an image thereon,characterized in that: a final surface of said beam-condensing opticalsystem, through which a light beam leaving said condensing opticalsystem is entered into said optical deflection means, and a firstsurface of said image-formation optical system, through which a lightbeam is entered from said optical deflection means into saidimage-formation optical system, are defined by the same surface.
 5. Thescanning optical system according to claim 4, characterized in thatoptically functional surfaces located before and after said opticaldeflection means are defined by transmitting surfaces.
 6. The scanningoptical system according to claim 4, characterized in that said opticalmember has at least one surface having a function of transmitting lightand a function of reflecting light.
 7. A scanning optical systemcomprising: a condensing optical system for collimating a light beamfrom a light source into a substantially parallel beam, an opticaldeflection means for deflecting light emerging from said condensingoptical system for scanning the surface to be scanned, and animage-formation optical system for focusing light deflected by saidoptical deflection means into the surface to be scanned, thereby formingan image thereon, characterized in that: said scanning optical systemcomprises a prism member, and said prism member includes at least aportion of said condensing optical system, and at least a portion ofsaid image-formation optical system.
 8. The scanning optical systemaccording to claim 7, characterized in that said condensing opticalsystem and said image-formation optical system are constructed of oneprism member.
 9. A scanning optical system according to claim 1, 4 or 7,comprising: a beam-condensing optical system for collimating a lightbeam from a light source into a substantially parallel beam, an opticaldeflection means for deflecting light emerging from said condensingoptical system for scanning the surface to be scanned, and animage-formation optical system for focusing light deflected by saidoptical deflection means into the surface to be scanned, thereby formingan image thereon, characterized in that: a total of at least threereflections occur at said condensing optical system and saidimage-formation optical system.
 10. The scanning optical systemaccording to claim 7, characterized in that said prism member comprisingat least a portion of said condensing optical system and at least aportion of said image-formation optical system has a combinedtransmitting and reflecting surface.
 11. The scanning optical systemaccording to claim 10, characterized in that said prism membercomprising at least a portion of said condensing optical system and atleast a portion of said image-formation optical system has a combinedsurface having three optical actions, two transmission actions and onereflection action.
 12. The scanning optical system according to claim 7,characterized in that: the portion of said condensing optical systemincluded in said prism member comprises at least three surfaces, anentrance surface for said prism member, a rotationally asymmetricreflecting surface that has optical power and is decentered with respectto an axial chief ray, and an exit surface from said prism member, andthe portion of said image-formation optical system included in saidprism member comprises at least three surfaces, a reentrance surface forsaid prism member, a rotationally asymmetric reflecting surface that hasoptical power and is decentered with respect to an axial chief ray, andan re-exit surface from said prism member.
 13. The scanning opticalsystem according to claim 1, 4 or 7, characterized in that said opticaldeflection means is a two-dimensional optical deflection means thateffects two-dimensional deflection at one optical deflection means.